A compact formula for the stress tensor inside a self-gravitating, triaxial ellipsoid in an arbitrary rotation state is given. It contains no singularity in the incompressible medium limit. The stress tensor and the quality factor model are used to derive a solution for the energy dissipation resulting in the damping (short axis mode) or excitation (long axis) of wobbling. In the limit of an ellipsoid of revolution, we compare our solution with earlier ones and show that, with appropriate corrections, the differences in damping times estimates are much smaller than it has been claimed. This version implements corrections of misprints found in the MNRAS published text.Comment: 14 pages, 6 figures, published in Monthly Notices RAS (containing misprints

The Double Asteroid Redirection Test (DART) spacecraft successfully performed the first test of a kinetic impactor for asteroid deflection by impacting Dimorphos, the secondary of near-Earth binary asteroid (65803) Didymos, and changing the orbital period of Dimorphos. A change in orbital period of approximately 7 min was expected if the incident momentum from the DART spacecraft was directly transferred to the asteroid target in a perfectly inelastic collision1, but studies of the probable impact conditions and asteroid properties indicated that a considerable momentum enhancement (β) was possible2,3. In the years before impact, we used lightcurve observations to accurately determine the pre-impact orbit parameters of Dimorphos with respect to Didymos4–6. Here we report the change in the orbital period of Dimorphos as a result of the DART kinetic impact to be −33.0 ± 1.0 (3σ) min. Using new Earth-based lightcurve and radar observations, two independent approaches determined identical values for the change in the orbital period. This large orbit period change suggests that ejecta contributed a substantial amount of momentum to the asteroid beyond what the DART spacecraft carried.

We have acquired simultaneous high-precision space photometry and radial velocities of the bright hybrid β Cep/SPB pulsator γ Peg. Frequency analyses reveal the presence of six g modes of high radial order together with eight loworder β Cep oscillations in both data sets. Mode identification shows that all pulsations have spherical degrees ℓ = 0 − 2. An 8.5 M ⊙ model reproduces the observed pulsation frequencies; all theoretically predicted modes are detected.We suggest, contrary to previous authors, that γ Peg is a single star; the claimed orbital variations are due to g-mode pulsation. γ Peg is the first hybrid pulsator for which a sufficiently large number of high-order g modes and low order p and mixed modes have been detected and identified to be usable for in-depth seismic modeling.

Context. As the ESA Rosetta mission approached, orbited, and sent a lander to comet 67P/Churyumov-Gerasimenko in 2014, a large campaign of ground-based observations also followed the comet. Aims. We constrain the total activity level of the comet by photometry and spectroscopy to place Rosetta results in context and to understand the large-scale structure of the comet's coma pre-perihelion. Methods. We performed observations using a number of telescopes, but concentrate on results from the 8 m VLT and Gemini South telescopes in Chile. We use R-band imaging to measure the dust coma contribution to the comet's brightness and UV-visible spectroscopy to search for gas emissions, primarily using VLT/FORS. In addition we imaged the comet in near-infrared wavelengths (JHK) in late 2014 with Gemini-S/Flamingos-2. Results. We find that the comet was already active in early 2014 at heliocentric distances beyond 4 au. The evolution of the total activity (measured by dust) followed previous predictions. No gas emissions were detected despite sensitive searches. Conclusions. The comet maintains a similar level of activity from orbit to orbit, and is in that sense predictable, meaning that Rosetta results correspond to typical behaviour for this comet. The gas production (for CN at least) is highly asymmetric with respect to perihelion, as our upper limits are below the measured production rates for similar distances post-perihelion in previous orbits.

Aims. Approach observations with the Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS) experiment onboard Rosetta are used to determine the rotation period, the direction of the spin axis, and the state of rotation of comet 67P's nucleus. Methods. Photometric time series of 67P have been acquired by OSIRIS since the post wake-up commissioning of the payload in March 2014. Fourier analysis and convex shape inversion methods have been applied to the Rosetta data as well to the available ground-based observations. Results. Evidence is found that the rotation rate of 67P has significantly changed near the time of its 2009 perihelion passage, probably due to sublimation-induced torque. We find that the sidereal rotation periods P 1 = 12.76129 ± 0.00005 h and P 2 = 12.4043 ± 0.0007 h for the apparitions before and after the 2009 perihelion, respectively, provide the best fit to the observations. No signs of multiple periodicity are found in the light curves down to the noise level, which implies that the comet is presently in a simple rotation state around its axis of largest moment of inertia. We derive a prograde rotation model with spin vector J2000 ecliptic coordinates λ = 65• ± 15• , corresponding to equatorial coordinates RA = 22• , Dec = +76• . However, we find that the mirror solution, also prograde, at λ = 275• ), is also possible at the same confidence level, due to the intrinsic ambiguity of the photometric problem for observations performed close to the ecliptic plane.

V440 Per is a Population I Cepheid with a period of 7.57 d and low‐amplitude, almost sinusoidal light and radial velocity curves. With no reliable data on the first harmonic, its pulsation mode identification remained controversial. We obtained a radial velocity curve of V440 Per with our new high‐precision and high‐throughput Poznań Spectroscopic Telescope. Our data reach an accuracy of 130 m s−1 per individual measurement and yield a secure detection of the first harmonic with an amplitude of A2= 140 ± 15 m s−1. The velocity Fourier phase φ21 of V440 Per is inconsistent at the 7.25σ level with those of fundamental‐mode Cepheids, implying that the star must be an overtone Cepheid, as originally proposed by Kienzle et al. Thus, V440 Per becomes the longest‐period Cepheid with securely established overtone pulsations. We show that a convective non‐linear pulsation hydrocode can reproduce the Fourier parameters of V440 Per very well. The requirement to match the observed properties of V440 Per constrains the free parameters of the dynamical convection model used in the pulsation calculations, in particular the radiative loss parameter.

The paper expands the idea of Vokrouhlický and Nesvorný who used a modified Zappalà et al. metric with osculating elements in search for pairs of asteroids suspected of having a common origin. Using six different orbital similarity functions, we find that five of them display a similar excess of close pairs in the catalogue of osculating elements. The excess is even higher when mean orbital elements are used. Similarly, when the mean elements are applied, there is a better agreement between the closest pairs found in the same catalogue using different metrics. The common subset of 62 pairs from five lists of 100 closest pairs according to different distance functions is provided. Investigating an artificial sample of asteroid orbital pairs with a known initial orbital velocity difference we find that the Drummond metric best preserves orbital proximity over long time intervals.

A semi-analytical model of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect on an asteroid spin in a non-principal axis rotation state is developed. The model describes the spin-state evolution in Deprit-Elipe variables, first-order averaged with respect to rotation and Keplerian orbital motion. Assuming zero conductivity, the YORP torque is represented by spherical harmonic series with vectorial coefficients, allowing us to use any degree and order of approximation. Within the quadrupole approximation of the illumination function we find the same first integrals involving rotational momentum, obliquity and dynamical inertia that were obtained by Cicaló & Scheeres. The integrals do not exist when higher degree terms of the illumination function are included, and then the asymptotic states known from Vokrouhlický et al. appear. This resolves an apparent contradiction between earlier results. Averaged equations of motion admit stable and unstable limit cycle solutions that were not previously detected. Non-averaged numerical integration by the Taylor series method for an exemplary shape of 3103 Eger is in good agreement with the semi-analytical theory.